The present invention relates to vibration damping of structures and, more particularly, to the monitoring and dynamic damping of vibrations in a structure by use of additional mass-spring-damper principle.
Engineering structures may be subject to loading conditions which result in displacements adversely affecting their desired performance. This is true with respect not only to static structures, but also moving structures such as motors, rotors and tools. The ensuing stresses due to these disturbances lead to fatigue and subsequent structural failure. As is generally agreed, the most detrimental form of loads are cyclical which cause a vibrational motion which may produce frequencies in the range of the natural frequency of vibration of the structure.
To reduce the deleterious effect of such vibrational motion, numerous methods have been proposed which may be generally grouped in two classes:
(a) Vibration Isolation. The structure is isolated from the input loads, i.e., the disturbances. PA1 (b) Vibration Absorption. A modification of the structure is made which makes it non-responsive to the anticipated input disturbances. This mentioned modification may range from a simple alteration of certain structural parameters (e.g., stiffness or damping) to the coupling of a secondary structure to the primary one. This secondary structure is referred to as a vibration absorber. Its purpose is to absorb the energy input of the disturbances, thus reducing their effect on the primary structure. PA1 (a) It is tunable to practically all possible frequencies of excitation, uniquely utilizing a partial state feedback. PA1 (b) This tuning can be done in real time.
Input disturbances are typically assumed to be harmonic forcing functions. The practicality of this selection results from the fact that any periodic disturbance may be analyzed as the sum of harmonic functions. Following this conventional analysis, the dynamic response of a structure is attenuated by use of a classical vibration absorber in the form of a mass-spring-damper as illustrated in FIG. 1. This absorber is attached to the primary structure imparting an additional degree of freedom. An absorber properly tuned to the vibrational frequency of the basic structure can highly attenuate the response of the primary system. A tuned absorber is defined as having values of m.sub.a, k.sub.a, and c.sub.a which yield maximum attenuation of oscillations of the primary structure, as described in many textbooks, e.g., Inman, D. J., Vibration: with Control, Measurement and Stability, 1989 Prentice-Hall, Englewood Cliffs, N.J.. Obviously, the ideal absorption in response to harmonic forcing is achieved by introducing an equal and opposite force. An excited spring-mass at its natural frequency, i.e., in resonance, could achieve this objective.
The tuned passive absorber is most effective to remove the undesired oscillations of the primary structure in a narrow and fixed interval of operating frequencies, mainly near the M.sub.peak of the absorber section and ideally with c.sub.a .apprxeq.0 setting. As a well known drawback, the effect of the absorber rapidly deteriorates outside of this range. If the excitation source is of varying frequency, there must be an absorber "tuned to these vibrations.
There have been numerous studies in the field of active and passive vibration absorption (or suppression). Some recent ones can be listed as Soong, T. T., Active Structural Control: Theory and Practice, 1990 Wiley, New York; Soong, T. T., Reinhorn, A. M., Wang, Y. P., Lin, R. C., Full-Scale Implementation of Active Control. I: Design and Simulation, Journal of Structural Engineering, 1991 Vol. 117, No. 11.; Yang, J. N., 1988, Recent Advances in Active Control of Civil Engineering Structures, Journal of Probabilistic Engineering Mechanics, Vol. 3 1991; Yang, B., Noncolocated Control of a Damped String Using Time Delay, Proceedings of the 1991 American Control Conference, Vol. 3, Boston, Mass.; Inman, D. J., 1989 Vibration: With Control, Measurement and Stability, Prentice-Hall, Englewood Cliffs, N.J.; Leipholz, H. H. E., and Abdel-Rohman, M., 1986 Control of Structures, Martinus Nijhoff, Dordrecht, The Netherlands. In essence, they propose a structural alteration to the primary system to interfere with the behavior of the primary body passively or to subdue actively its vibratory response. All of these techniques are quite effective in their objectives. Briefly, the modified dynamic mechanisms absorb the energy input of the excitation source of the structure.
An essential requirement for this absorption property is that it should be equally effective for a large band of operating frequencies, i.e., it should be tunable without sacrificing the quality of performance. To indicate the practical applications of this "frequency tuning" feature, machine tool vibrations (at the tool-workpiece interface), aircraft fuselage parts, submersible hulls, and lively civic structures are subject to variations in vibrational frequency. Because of the excitation frequency variations imposed on these systems, the absorption must be frequency tuned dynamically to be effective. Most of the earlier techniques fail to respond to this requirement, Those which succeed necessitate time consuming mechanical changes (e.g., Soong, 1991, supra); thus, they are not suitable for practical applications.
This fertile area of engineering is enjoying the advent of new proposals, generally based on computerized active control methods. One recent development in this field is the concept of "Delayed Resonators" (DR) which utilizes position feedback with a controlled time delay as described in Olgac, N., McFarland, D. M., Holm-Hansen, B., Position Feedback-Induced Resonance: The Delayed Resonator, DSC--Volume 38, Active Control of Noise and Vibration, ASME-WAM 1992. The originality of this methodology is multifaceted:
The structure shown in FIG. 2 represents a single degree of freedom (SDOF) absorber with an additional feedback force gx.sub.a (t-.tau.), where g is a feedback gain and .tau. is a time delay applied to the displacement x.sub.a. Control strategies involving time delay have been considered extensively in the literature, and almost all of them treat time delay as an undesirable property of the dynamics, to be either eliminated or compensated in B. Yang, Noncollocated Control Of A Damped String Using Time Delay, Proceedings of the 1991 American Control Conference 3, 1991, 2445-2448, Noncollocated control of a damped string using time delay, M. Abdel-Mooty and J. Roorda, Time Delay Compensation In Active Damping Of Structures, Journal of Engineering Mechanics 117, 1991, 2549-2570, and J. Rodeliar, L. L. Chung, T. T. Soong and A. M. Reinhorn, Experimental Digital Control Of Structures, Journal of Engineering Mechanics 115, 1989, 1245-1261. The stability aspects of such systems with inherent time delay have also been widely studied in N. Olgac and W. Youping, On The Stability of Linear Systems With Unrelated Time Delays, ASME International Computers in Engineering Conference, 1989, K. Youcef-Toumi and O. Ito, A Time Delay Controller For Systems With Unknown Dynamics, Transactions of the American Society of Mechanical Engineers, Journal of Dynamic Systems, Measurement, and Control 112, 1990, 133-142, and W. J. Wang, C. C. Kao and C. S. Chen, Stabilization, Estimation and Robustness For Large Scale Time-Delay Systems, Control-Theory and Advanced Technology 7, 1991, 569-585. These investigations are almost exclusively initiated to compensate for the delayed response behavior of sensors or actuators.
Since it is a destabilizing factor, delay is seldom intentionally introduced into the system dynamics. An interesting treatment of time delay in the control is given by Yang 1991 supra in an effort to stabilize the non-collocated control of a damped string wherein the propagation delay between the sensor and the actuator must be compensated. However, the propagation delay is still an inherent feature of the dynamics.
Time delay has been proposed as a control design element by K. Youcef-Toumi and J. Bobbett, Stability Of Uncertain Linear Systems With Time Delay, Transactions of the American Society of Mechanical Engineers, Journal of Dynamic Systems, Measurements and Control 113, 1991, 558-567, in which an uncertain linear system is stabilized by a delayed state feedback, using Kharitonov and Nyquist philosophies.
It is an object of the present invention to provide a novel method for dynamically damping vibrations of a structure under various applied loads by use of controlled time delay in the feedback controlling a damping member.
It is also an object to effect such damping by delayed resonation of the damping member.
Another object is to provide novel apparatus for dynamically damping vibrations in a monitored structure under varying applied loads by use of controlled time delay.